In Quadrature Amplitude Modulation (QAM) techniques both amplitude and phase are used to represent the data contained within the signal. Often 8-QAM to 256-QAM systems are used in applications such as wireline communications. Data is transmitted in a QAM modulation scheme with the data contained within the amplitude and phase of the transmitted signal. In a typical system, for every n bits of data, a QAM symbol (Ik, Qk) is generated using some constellation encoder, where Ik is the kth real amplitude and Qk is the kth imaginary amplitude of the signal. In conventional systems, the signal is transmitted through a modulator which converts the signal into analog waveform for transmission through a channel to a remote location. The remote location includes a demodulator which converts the received analog waveform into a QAM constellation point, and a constellation decoder which converts the QAM constellation point back into n bits.
Usually the constellation encoder-decoder elements are designed to correct for phase ambiguities in the received QAM constellation point. See, for example, U.S. Pat. No. 5,233,630, the entirety of which is incorporated herein by reference. Overlooked, however, is the effect of spectral inversion or "mirroring" across an axis (typically, the I axis). This occurs, for example, when the signal is frequency stacked such as in cable modem system.
Thus, there is a need to design encoder-decoder elements in a constellation system that correct for spectral inversion.